Walmart Weekly Sales Forecasting: Model Comparison

1 Objective

This report compares six forecasting approaches for weekly Walmart sales:

1. Local Linear Anomaly Model (Phase 1).
2. Bayesian Structural AR (Phase 2, full data).
3. Elastic Net anomaly baseline (Phase 3).
4. Random Forest anomaly baseline (Phase 4).
5. ETS anomaly baseline (Phase 5).
6. AdaBoost anomaly baseline (Phase 7).

Additionally, we include a Phase 1-lite diagnostic variant in the final comparison to show the impact of removing the extra exogenous variables from Local Linear.

Evaluation uses forward-chaining validation and weighted MAE (WMAE).

2 Data and Evaluation Setup

	Artifact	Value
0	Phase 1 OOF rows	154386
1	Phase 1-lite OOF rows	154386
2	Phase 2 OOF rows	154386
3	Elastic Net OOF rows	154386
4	Random Forest OOF rows	154386
5	ETS OOF rows	154386
6	AdaBoost OOF rows	154386

Validation metric:

\[ \text{WMAE} = \frac{\sum_i w_i \lvert y_i - \hat{y}_i \rvert}{\sum_i w_i}, \quad w_i = \begin{cases} 5, & \text{if holiday} \\ 1, & \text{otherwise} \end{cases} \]

3 Model 1: Local Linear Anomaly (Phase 1)

Local Linear is a weighted regression that learns a different local coefficient vector for each week-of-year neighborhood and each series. It is simple and interpretable, but sensitive to feature scaling, so standardization is applied before fitting.

3.1 Mathematical Formulation

For series (s) and target seasonal week (w):

\[ \hat{\beta}_{s,w} = \arg\min_{\beta} \sum_{i \in s} K_h\!\left(d(\text{week}_i,w)\right) \left(y_i - \beta_0 - x_i^\top \beta\right)^2 + \lambda \|\beta\|_2^2 \]

and recursive prediction:

\[ \hat{y}^{anom}_{t,s}=\beta_0 + x_{t,s}^\top \beta,\qquad \hat{y}_{t,s}=\hat{y}^{anom}_{t,s}+clim_{t,s} \]

3.2 Plain-Language Meaning of Terms

• series s: one specific Store + Dept time series.
• week_i and w: historical week index and target seasonal week where local fitting is centered.
• K_h(d(.)): a weight that gives more importance to rows close in seasonal calendar (e.g., nearby weeks of year).
• x_i: the input features for a row (lags, holiday flag, exogenous variables).
• beta_0, beta: intercept and coefficients learned by local weighted regression.
• lambda: regularization strength that shrinks coefficients to avoid unstable fits.
• y^{anom}: anomaly target (real sales minus climatology baseline).
• clim_{t,s}: baseline seasonal level added back to convert anomaly prediction to sales prediction.

3.3 Workflow

flowchart LR
  A[Read train/test parquet] --> B[Compute climatology per series/store/week]
  B --> C[Create anomalies and lag1/lag2]
  C --> D[Impute missing lag/exogenous values]
  D --> E[Standard-scale Phase 1 features]
  E --> F[Forward-chaining CV]
  F --> G[Fit local weighted ridge by series and seasonal week]
  G --> H[Recursive rollout on validation horizon]
  H --> I[OOF metrics and predictions]
  I --> J[Fit full train and forecast test]

3.4 Tuned Parameters and Effect

	Parameter	Value	How it works
0	kernel	tricube	Kernel shape over seasonal distance; controls ...
1	bandwidth	6	Neighborhood width in week-of-year units; larg...
2	min_samples	16	Minimum active samples to fit a local model; g...
3	ridge	0.0001	L2 regularization strength in weighted regress...
4	coef_clip	6.0	Post-fit coefficient clipping to prevent extre...
5	anom_clip_scale	2.0	Prediction clipping band around anomaly quanti...
6	lags	[1, 2]	Autoregressive inputs used in recursive foreca...
7	standard_scaler	True	Feature standardization before fitting local r...

{'kernel': 'tricube',
 'bandwidth': 6,
 'min_samples': 16,
 'ridge': 0.0001,
 'coef_clip': 6.0,
 'anom_clip_scale': 2.0,
 'lags': [1, 2],
 'use_interactions': False,
 'interaction_cols': [],
 'feature_cols': ['temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment',
  'sales_anom_lag1',
  'sales_anom_lag2',
  'is_holiday_int'],
 'standard_scaler': True,
 'n_folds': 4,
 'val_weeks': 13,
 'max_series': None}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	5989.774614	5916.085624	11465.394577
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	10061.944470	10472.387681	20457.695819
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	11956.737489	11956.737489	21420.299578
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	12294.668865	12479.604773	22343.880598

wmae     10075.78136
mae     10206.203892
rmse    18921.817643
Name: 4, dtype: object

4 Model 1-lite: Local Linear Diagnostic Variant

Phase 1-lite keeps the same Local Linear method but removes the extra exogenous variables (MarkDown1-5, CPI, Unemployment) and uses only temp_anom, fuel_anom plus lags/holiday.

{'kernel': 'tricube',
 'bandwidth': 6,
 'min_samples': 16,
 'ridge': 0.0001,
 'coef_clip': 6.0,
 'anom_clip_scale': 2.0,
 'lags': [1, 2],
 'feature_mode': 'lite',
 'exogenous_features': ['temp_anom', 'fuel_anom'],
 'use_interactions': False,
 'interaction_cols': [],
 'feature_cols': ['temp_anom',
  'fuel_anom',
  'sales_anom_lag1',
  'sales_anom_lag2',
  'is_holiday_int'],
 'standard_scaler': True,
 'n_folds': 4,
 'val_weeks': 13,
 'max_series': None}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	2468.567458	2271.802436	4955.291247
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	2199.682469	2196.184633	4485.720535
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	2028.753667	2028.753667	3948.262807
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	1947.742271	1923.235682	3954.874629

wmae    2161.186467
mae     2104.994105
rmse    4336.037305
Name: 4, dtype: object

5 Model 2: Bayesian Structural AR (Phase 2)

Structural AR combines hierarchical intercepts, autoregressive lags, exogenous drivers, and seasonal Fourier terms in one probabilistic model. It is designed to capture both shared structure and series-specific behavior.

5.1 Mathematical Formulation

In z-score space:

\[ y^{*}_{t,s} \sim \mathcal{N}(\mu_{t,s}, \sigma) \]

\[ \mu_{t,s} = \alpha_s + \beta_{lag}^\top lag_{t,s} + \beta_{exog}^\top exog_{t,s} + \beta_h h_{t,s} + \beta_{tr} trend_t + \beta_f^\top fourier_t \]

with hierarchical intercept:

\[ \alpha_s = \alpha_\mu + \alpha_\sigma z_s,\qquad z_s \sim \mathcal{N}(0,1) \]

5.2 Plain-Language Meaning of Terms

• y*_{t,s}: normalized anomaly target for week t and series s.
• mu_{t,s}: model mean prediction before adding random noise.
• alpha_s: series-specific baseline level; each Store + Dept has its own intercept.
• beta_lag, lag_{t,s}: coefficients and lag features that capture autoregressive behavior.
• beta_exog, exog_{t,s}: effects of external drivers (temperature, markdown flags, CPI, unemployment, etc.).
• beta_h h_{t,s}: holiday contribution.
• beta_tr trend_t: long-run drift over time.
• beta_f fourier_t: smooth yearly seasonal pattern via sine/cosine terms.
• sigma: predictive noise level around the mean.

5.3 Workflow

flowchart LR
  A[Read train parquet] --> B[Compute climatology]
  B --> C[Create anomaly target and lag1/lag2]
  C --> D[Build trend and Fourier seasonal terms]
  D --> E[Fill exogenous NA from train medians]
  E --> F[Standardize lag/exogenous/trend variables]
  F --> G[Fit PyMC structural model via MAP]
  G --> H[Recursive probabilistic rollout by date]
  H --> I[Aggregate draws to mean/sd and intervals]
  I --> J[CV metrics and OOF outputs]

5.4 Tuned Parameters and Effect

	Parameter	Value	How it works
0	max_eval	1800	Maximum evaluations in MAP optimization; highe...
1	pred_draws	40	Number of stochastic recursive draws for predi...
2	fourier_order	3	Number of sine/cosine seasonal harmonics.
3	lag_orders	[1, 2]	Autoregressive lags used as structural predict...
4	sigma_clusters	0	Number of heteroskedastic noise clusters; 0 me...
5	exogenous_features	[temp_anom, fuel_anom, MarkDown1, MarkDown2, M...	External covariates entering the structural mean.

{'n_folds': 4,
 'val_weeks': 13,
 'max_eval': 1800,
 'random_seed': 8927,
 'pred_draws': 40,
 'fourier_order': 3,
 'lag_orders': [1, 2],
 'exogenous_features': ['temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment'],
 'sigma_clusters': 0,
 'max_series': 3331,
 'note': 'Structural AR model with hierarchical series intercept, trend, Fourier seasonality, and recursive validation.'}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse	runtime_sec
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	2514.047613	2354.646140	4935.317829	64.718200
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	2192.877850	2207.494598	4400.426532	68.368072
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	2138.504577	2138.504577	3799.486079	68.047948
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	1904.502883	1885.828366	3620.883291	65.612177

wmae           2187.483231
mae             2146.61842
rmse           4189.028433
runtime_sec      66.686599
Name: 4, dtype: object

6 Model 3: Elastic Net Anomaly Baseline (Phase 3)

Elastic Net is a linear model with combined L1/L2 regularization. It is a robust baseline for correlated tabular features and keeps an interpretable global linear structure.

6.1 Mathematical Formulation

\[ \hat{\beta} = \arg\min_{\beta} \frac{1}{2n}\|y - X\beta\|_2^2 + \alpha\left( \frac{1-l1\_ratio}{2}\|\beta\|_2^2 + l1\_ratio\|\beta\|_1 \right) \]

6.2 Plain-Language Meaning of Terms

• X beta: linear combination of all features.
• ||y - X beta||^2: fit error term (how far predictions are from truth).
• alpha: total regularization strength.
• l1_ratio: balance between:
• L1 penalty: pushes less-useful coefficients to exactly zero (feature selection behavior).
• L2 penalty: smoothly shrinks coefficients for stability under correlated features.

6.3 Workflow

flowchart LR
  A[Read train/test parquet] --> B[Compute climatology and anomalies]
  B --> C[Create lag1/lag2 and calendar features]
  C --> D[Build exogenous feature matrix]
  D --> E[Median imputation + standard scaling]
  E --> F[Fit Elastic Net on train folds]
  F --> G[Recursive forecasting on validation horizon]
  G --> H[OOF metrics and predictions]
  H --> I[Fit full train and forecast test]

6.4 Tuned Parameters and Effect

	Parameter	Value	How it works
0	alpha	0.02	Overall regularization strength; larger values...
1	l1_ratio	0.2	Mix between L1 (sparsity) and L2 (stability).
2	max_iter	10000	Maximum coordinate-descent iterations for conv...
3	lags	[1, 2]	Lag features used in recursive setup.
4	features	[lag1, lag2, week_of_year, month, is_holiday_i...	Full tabular interface for model fitting.

{'model': 'elastic_net',
 'target': 'sales_anom',
 'features': ['lag1',
  'lag2',
  'week_of_year',
  'month',
  'is_holiday_int',
  'temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment'],
 'lags': [1, 2],
 'alpha': 0.02,
 'l1_ratio': 0.2,
 'max_iter': 10000,
 'n_folds': 4,
 'val_weeks': 13,
 'max_series': None,
 'train_path': 'train_feat.parquet',
 'test_path': 'test_feat.parquet'}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse	runtime_sec
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	2472.678568	2292.791482	4919.584363	6.225060
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	2163.772249	2175.479837	4420.761374	8.105888
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	2058.784472	2058.784472	3793.832714	7.717091
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	1833.856224	1803.861985	3645.865425	12.398858

wmae           2132.272878
mae            2082.729444
rmse           4195.010969
runtime_sec       8.611724
Name: 4, dtype: object

7 Model 4: Random Forest Anomaly Baseline (Phase 4)

Random Forest is an ensemble of decision trees trained on bootstrap samples. It captures nonlinear interactions with little feature engineering and is robust to mixed feature scales.

7.1 Mathematical Formulation

For (B) trees:

\[ \hat{y}(x)=\frac{1}{B}\sum_{b=1}^{B} T_b(x) \]

where each (T_b) is grown on a bootstrap sample and split candidates are randomized via max_features.

7.2 Plain-Language Meaning of Terms

• T_b(x): prediction from tree b.
• B: number of trees in the forest.
• Final prediction is an average of trees, which reduces variance and improves robustness.
• Bootstrap sampling means each tree sees a slightly different sampled training set.
• Random split-feature selection (max_features) decorrelates trees, improving ensemble quality.

7.3 Workflow

flowchart LR
  A[Read train/test parquet] --> B[Compute climatology and anomalies]
  B --> C[Create lag1/lag2 + calendar + exogenous features]
  C --> D[Median imputation]
  D --> E[Train Random Forest on fold train]
  E --> F[Recursive multi-step rollout on fold validation]
  F --> G[OOF metrics and predictions]
  G --> H[Refit on full train and forecast test]

7.4 Tuned Parameters and Effect

	Parameter	Value	How it works
0	n_estimators	120	Number of trees; larger reduces variance but i...
1	max_depth	18	Maximum tree depth; controls model complexity.
2	min_samples_leaf	2	Minimum samples per leaf; regularizes tree par...
3	max_features	sqrt	Feature subset size considered at each split.
4	lags	[1, 2]	Autoregressive lag features used recursively.

{'model': 'random_forest',
 'target': 'sales_anom',
 'features': ['lag1',
  'lag2',
  'week_of_year',
  'month',
  'is_holiday_int',
  'temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment'],
 'lags': [1, 2],
 'n_estimators': 120,
 'max_depth': 18,
 'min_samples_leaf': 2,
 'max_features': 'sqrt',
 'n_folds': 4,
 'val_weeks': 13,
 'max_series': None,
 'train_path': 'train_feat.parquet',
 'test_path': 'test_feat.parquet'}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse	runtime_sec
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	2443.770022	2243.909149	4898.711983	14.831643
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	2132.907277	2148.134375	4393.405264	20.781198
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	1915.343992	1915.343992	3675.397679	19.938103
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	1738.982368	1719.540629	3554.458799	19.019421

wmae           2057.750915
mae            2006.732036
rmse           4130.493432
runtime_sec      18.642591
Name: 4, dtype: object

8 Model 5: ETS Anomaly Baseline (Phase 5)

ETS here is used on residual anomalies after removing an exogenous linear component. This hybrid keeps classical exponential smoothing dynamics while allowing external regressors to explain systematic variation.

8.1 Mathematical Formulation

Exogenous residual decomposition:

\[ y^{anom}_{t,s}=g(x_{t,s}) + r_{t,s},\qquad g(\cdot)\text{ from Ridge regression} \]

Residual component (r_{t,s}) is modeled by ETS:

\[ r_{t,s} = \ell_{t-1,s}+b_{t-1,s}+s_{t-m,s}+\varepsilon_{t,s} \]

and final forecast:

\[ \hat{y}_{t,s}=clim_{t,s}+\hat{g}(x_{t,s})+\hat{r}_{t,s} \]

8.2 Plain-Language Explanation (What ETS Is)

ETS stands for Error, Trend, Seasonality. It is a classical time-series model that keeps three internal states and updates them week by week:

• level: the current baseline sales level for the series.
• trend: the direction/slope (increasing or decreasing behavior).
• seasonality: repeating seasonal pattern (here around yearly weekly cycle).

In this project we first predict the anomaly using exogenous variables (g(x)), then ETS models the remaining residual pattern (r). The final prediction is:

• exogenous part
• plus ETS residual dynamics
• plus climatology baseline to return to sales scale.

8.3 Plain-Language Meaning of Terms

• y^{anom}: anomaly sales target.
• g(x): exogenous linear predictor (Ridge) from external variables.
• r_{t,s}: residual anomaly after removing exogenous part.
• ell: level state.
• b: trend state.
• s: seasonal state.
• epsilon: random error term.

8.4 Workflow

flowchart LR
  A[Read train/test parquet] --> B[Compute climatology and anomalies]
  B --> C[Fit exogenous Ridge on anomaly target]
  C --> D[Compute residual anomaly = target - exogenous prediction]
  D --> E[Fit per-series ETS on residuals with fallback candidates]
  E --> F[Recursive fold forecasting by series]
  F --> G[Add exogenous component + climatology back]
  G --> H[OOF metrics and test forecasts]

8.5 Tuned Parameters and Effect

	Parameter	Value	How it works
0	seasonal_periods	52	Season length used by ETS seasonal state.
1	exog_alpha	1.0	Ridge penalty for exogenous linear component.
2	exogenous_features	[temp_anom, fuel_anom, MarkDown1, MarkDown2, M...	Regressors used before ETS residual modeling.
3	n_folds	4	Forward-chaining fold count.
4	val_weeks	13	Validation horizon length per fold.

{'model': 'ets',
 'target': 'sales_anom (via exogenous + ETS residual)',
 'seasonal_periods': 52,
 'exogenous_features': ['temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment'],
 'exog_alpha': 1.0,
 'n_folds': 4,
 'val_weeks': 13,
 'max_series': None,
 'cv_mode_counts': {'level': 10599,
  'level-trend': 1796,
  'global-fallback': 77,
  'last-value-fallback': 51,
  'level-seasonal': 4},
 'test_mode_counts': {'level': 2758,
  'level-trend': 372,
  'level-seasonal': 8,
  'global-fallback': 11,
  'last-value-fallback': 20},
 'train_path': 'train_feat.parquet',
 'test_path': 'test_feat.parquet'}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse	runtime_sec
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	2350.860561	2193.524621	4865.080883	137.155356
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	1965.952051	1969.586155	4035.608919	839.189260
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	1585.766265	1585.766265	3052.148316	952.329147
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	1436.435312	1435.277361	2961.666930	974.137173

wmae           1834.753547
mae              1796.0386
rmse           3728.626262
runtime_sec     725.702734
Name: 4, dtype: object

9 Model 6: AdaBoost Anomaly Baseline (Phase 7)

AdaBoost builds an additive ensemble of shallow trees, where each stage focuses more on difficult residual patterns from previous stages.

9.1 Mathematical Formulation

With base learners (h_m):

\[ F_M(x)=\sum_{m=1}^{M}\nu_m h_m(x) \]

where stage weights depend on chosen boosting loss and learning rate. In practice here, (h_m) are depth-limited regression trees.

9.2 Plain-Language Meaning of Terms

• h_m(x): base learner at stage m (small regression tree).
• nu_m: effective contribution of stage m to the final prediction.
• M: number of boosting stages.
• learning_rate: shrinkage factor that controls how aggressively each stage updates the model.
• Boosting logic: each new tree focuses more on errors made by previous trees.

9.3 Workflow

flowchart LR
  A[Read train/test parquet] --> B[Compute climatology and anomaly target]
  B --> C[Create lag1/lag2 + calendar + exogenous features]
  C --> D[Median imputation]
  D --> E[Train AdaBoost regressor on fold train]
  E --> F[Recursive validation rollout]
  F --> G[OOF metrics and predictions]
  G --> H[Refit on full train and produce test forecasts]

9.4 Tuned Parameters and Effect

	Parameter	Value	How it works
0	n_estimators	300	Number of boosting stages.
1	learning_rate	0.03	Shrinkage per stage; smaller needs more estima...
2	max_depth	3	Depth of each base regression tree.
3	loss	linear	Boosting loss that controls how hard examples ...
4	lags	[1, 2]	Autoregressive lag inputs for recursive foreca...

{'model': 'adaboost',
 'target': 'sales_anom',
 'features': ['lag1',
  'lag2',
  'week_of_year',
  'month',
  'is_holiday_int',
  'temp_anom',
  'fuel_anom',
  'MarkDown1',
  'MarkDown2',
  'MarkDown3',
  'MarkDown4',
  'MarkDown5',
  'CPI',
  'Unemployment'],
 'lags': [1, 2],
 'n_estimators': 300,
 'learning_rate': 0.03,
 'max_depth': 3,
 'loss': 'linear',
 'n_folds': 4,
 'val_weeks': 13,
 'max_series': None,
 'train_path': 'train_feat.parquet',
 'test_path': 'test_feat.parquet'}

	fold	train_start	train_end	val_start	val_end	wmae	mae	rmse	runtime_sec
0	1	2010-02-05	2011-10-28	2011-11-04	2012-01-27	2479.961992	2278.508843	4905.691398	144.954249
1	2	2010-02-05	2012-01-27	2012-02-03	2012-04-27	2197.511715	2189.320166	4409.023648	189.685843
2	3	2010-02-05	2012-04-27	2012-05-04	2012-07-27	2014.048705	2014.048705	3866.751795	214.710872
3	4	2010-02-05	2012-07-27	2012-08-03	2012-10-26	1865.985156	1843.294438	3739.207824	239.991155

wmae           2139.376892
mae            2081.293038
rmse           4230.168666
runtime_sec      197.33553
Name: 4, dtype: object

10 Final Comparative

10.1 Full-Data Comparison (Phases 1, 2, 3, 4, 5, 7 + Phase 1-lite Diagnostic)

	Model	Mean WMAE	Mean MAE	Mean RMSE
0	ETS (Phase 5)	1834.753547	1796.038600	3728.626262
1	Random Forest (Phase 4)	2057.750915	2006.732036	4130.493432
2	Elastic Net (Phase 3)	2132.272878	2082.729444	4195.010969
3	AdaBoost (Phase 7)	2139.376892	2081.293038	4230.168666
4	Local Linear Lite (Phase 1-lite)	2161.186467	2104.994105	4336.037305
5	Structural AR (Phase 2)	2187.483231	2146.618420	4189.028433
6	Local Linear Anomaly (Phase 1)	10075.781360	10206.203892	18921.817643

11 Conclusion

• Full-data comparison is now apples-to-apples for all six models.
• All tabular baselines share the same anomaly feature interface with lag1 and lag2.
• The ranking table above is the reference for selecting the best model in this run.